Prime Factors 

Webster defines prime as:

prime (prim) n.[ME, fr. MF, fem. of prin first, L primus; akin to L prior] 1 :first in time: original 2 a : having no factor except itself and one $\langle$3 is a   number $\rangle$ b : having no common factor except one $\langle$ 12 and 25 are relatively  $\rangle$ 3 a : first in rank, authority or significance : principal b : having the highest quality or value $\langle$  television time $\rangle$ [from Webster's New Collegiate Dictionary]

The most relevant definition for this problem is 2a: An integer g>1 is said to be prime if and only if its only positive divisors are itself and one (otherwise it is said to be composite). For example, the number 21 is composite; the number 23 is prime. Note that the decompositon of a positive number g into its prime factors, i.e.,

$$g = f_1 \times f_2 \times \dots \times f_n$$

is unique if we assert that f_i > 1 for all i and $f_i \le f_j$ for i<j.

One interesting class of prime numbers are the so-called Mersenne primes which are of the form 2^p- 1. Euler proved that 2³¹ - 1 is prime in 1772 -- all without the aid of a computer.

Input 

The input will consist of a sequence of numbers. Each line of input will contain one number g in the range -2³¹ < g <2³¹, but different of -1 and 1. The end of input will be indicated by an input line having a value of zero.

Output 

For each line of input, your program should print a line of output consisting of the input number and its prime factors. For an input number $g>0, g = f_1 \times f_2 \times \dots \times f_n$, where each f_i is a prime number greater than unity (with $f_i \le f_j$ for i<j), the format of the output line should be

$$g \mbox{\tt\ = } f_1 \mbox{\tt\ x } f_2 \mbox{\tt\ x } \dots \mbox{\tt\ x } f_n$$

When g < 0, if $\mid g \mid = f_1 \times f_2 \times \dots \times f_n$, the format of the output line should be

$$g \mbox{\tt\ = -1 x } f_1 \mbox{\tt\ x } f_2 \mbox{\tt\ x } \dots \mbox{\tt\ x } f_n$$

Sample Input 

-190
-191
-192
-193
-194
195
196
197
198
199
200
0

Sample Output 

-190 = -1 x 2 x 5 x 19
-191 = -1 x 191
-192 = -1 x 2 x 2 x 2 x 2 x 2 x 2 x 3
-193 = -1 x 193
-194 = -1 x 2 x 97
195 = 3 x 5 x 13
196 = 2 x 2 x 7 x 7
197 = 197
198 = 2 x 3 x 3 x 11
199 = 199
200 = 2 x 2 x 2 x 5 x 5